A canonical imaging system that may be used to explain the concept of an imaging system focus error, is shown in FIG. 1.
The FIG. 1A imaging system 10 comprises a conventional lens 12. Radiation rays 14, which represent parallel incident radiation beams from a fixed and infinite object point 16, are reflected by the lens 12 and converge to a focus F at a focal point 18. The focal point 18 is a sub-set of a focal plane 20 which intersects the focal point 18.
By definition, the focal point 18 is the image of the fixed and infinite object point 16. Accordingly, if a radiation detector 22, for example (and where appropriate), a photographic film, is placed coincident with the focal plane 20, the image of the fixed object point 16 at an imaging plane 24 defined by the radiation detector 22, can be sharply developed by the radiation detector 22.
In summary, the FIG. 1A imaging system 10 has been so constructed (i.e., with the focal plane 20 coincident with the imaging plane 24) that it does not introduce focus error: it is in-focus. An indicia of this desired condition is that the fixed and infinite object point 16 can be sharply developed, i.e., without undue blurs, fuzziness or other degradations of the image.
Attention is now directed to FIG. 1B, which shows a first modification of the FIG. 1A imaging system 10, so that a first out-of-focus condition can be demonstrated. Here, the imaging plane 24 has been physically displaced, by a distance D, from the focal plane 20. The physical displacement D corresponds to an introduction of focus error, and thus introduces a "sensible" and undesirable degradation of the image quality of the object point 16.
Attention is now directed to FIG. 1C, which shows a second modification of the FIG. 1A imaging system 10, so that a second out-of-focus condition can be demonstrated. Here, the focal plane 20 is still coincident with the imaging plane 24, but the heretofore fixed and infinite object point 16 has been displaced so that it is now located at a finite distance from the imaging system 10. This relocation action induces an out-of-focus condition, D, thereby introducing a sensible and undesirable image degradation.
Note, although not shown in FIG. 1, that an out-of-focus condition can also be induced by inter alia: changes in the lens 12 curvature, or temperature gradients incurred by the imaging system 10. In all cases, it is desired to determine a focus error for an out-of-focus condition, so that the imaging system can be efficiently restored to the in-focus state, thus providing sharp images of an object.
U.S. Pat. No. 5,166,506 issued in the name of Fiete et al. discloses a method for determining an imaging system focus error. That method employs a focus sensor and accompanying reference curve. However, that method samples three different focus positions to use as a basis for generating a parabolic curve, whereby the maximum of the parabolic curve is a measure of the imaging system focus error. Utilizing a parabolic curve provides reasonable results for small focus errors. However, either as focus error increases, or as the system response changes due to effects such as component aging or varying conditions of use or environment, the parabolic curve proves to be an inadequate representation of the true focus error from the point of optimum focus. As such, the parabolic curve does not accurately represent the full range of sensor response to various focus positions.